The term "Ajax" was publicly stated on 18 February 2005 by Jesse James Garrett in an article
titled "Ajax: A New Approach to Web Applications", based on techniques used on Google pages.

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Ajax is a client-side script that communicates to and from a server/database without the need for a postback
or a complete page refresh. The best definition I've read for Ajax is “the method of exchanging data with a server,
and updating parts of a web page without reloading the entire page.”

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But it is not browser compatible alone so it has to work with HTML and CSS for presentation, The Document Object Model (DOM)
for dynamic display of and interaction with data, XML/JASON for the interchange of data and XSLT for its manipulation,
The XMLHttpRequest object for asynchronous communication, JavaScript to bring these technologies together.

AJAX is a lightweight, Load faster, Solve lot of problems on server side without whole page refresh
but only part of web page so less load on servers,
Instant output on any activity, Great user interface etc.

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You can create, update, edit, records into database without refresh page.
(as Google search engine, Facebook are using it)